This invention relates to the game of pool or pocket billiards. More particularly, this invention relates to assemblies, and methods which assist in the training of pool players in performance of xe2x80x9ccut shotsxe2x80x9d.
One of the objects of the game of pool or pocket billiards is to utilize a pool cue to propel a cue ball over a pool table""s surface into contact with a pool ball, driving the pool ball forwardly into one of the pool table""s pockets. When a cue ball successfully drives a pool ball into a pocket, the cue ball typically strikes the pool ball at a ball strike point prescribed by geometries of the ball and the table. Since cue balls and pool balls are typically commonly sized, having equal diameters, the ball strike point is typically located on the surface of the pool ball, and is further located a distance above the pool table""s surface equal to the radius of the pool ball. The proper ball strike point is further located by a flat vertical reference plane which bisects the pool ball and which extends forwardly from the pool ball to intersect the opening of the pocket into which the pool ball is to be driven. The proper ball strike point lies within such reference plane and on the rearward side of the pool ball. The proper ball strike point remains the same regardless of whether the cue ball is to be driven in an angled cut shot or a straight xe2x80x9cin linexe2x80x9d shot.
Where an xe2x80x9cin linexe2x80x9d shot is to be performed, the pool player may cause the cue ball to properly strike the pool ball at the ball strike point by aiming a pool cue stroke so that the pool cue drives the cue ball directly toward the center of the pool ball. Accordingly, where an xe2x80x9cin linexe2x80x9d shot is to be performed, the profile of the pool ball itself provides a useful aiming target.
In contrast, where an angled cut shot must be performed, the profile of the pool ball ceases to provide a useful aiming target. In performing a cut shot, neither the pool ball to be struck, nor any visible feature of the pool table serves as a useful aiming target. Accordingly, in performing a pool cut shot, a pool player must undesirably aim a pool cue stroke to drive the cue ball toward a target point which is not defined by any visible structure or indicia.
The instant inventive assembly and method for cut shooting a pool ball solves or ameliorates the above described drawback or difficulty by providing assemblies and method steps which result in illumination of a concise, visible point upon the pool table""s surface, such illuminated point serving as a cut shot target point.
Through repeated use of the instant inventive assembly and method, a novice pool player may become better able to perform cut shots without the provision of an illuminated cut shot target point.
A major structural component of the assembly of the instant invention comprises a support frame for elevating, holding and pointing light beam emitters, preferably lasers. Preferably, the support frame comprises an enlarged base having a columnar hollow housing extending upwardly therefrom, the preferred lasers each being supported thereon in a double shear fashion by laterally opposed side walls of the columnar housing. Suitably, the upwardly extending portion of the frame may alternately comprise a single bar or post which supports the lasers in a cantilevered fashion.
The geometry explaining the function of the assembly of the instant invention is best envisioned with reference to a vertically oriented plane extending perpendicularly upwardly from a pool table""s surface. Such reference plane vertically bisects a pool ball resting upon the table surface and extends forwardly from the pool ball to intersect the opening of a pocket into which a pool ball is to be driven. The frame preferably supports a ball spotting laser at an elevation above the pool table""s surface and, preferably, the frame is positionable so that a rearward extension of the reference plane from the pool ball may bisect the ball spotting laser. As a result of such positioning, a ball spotting laser light beam emitted by the ball spotting laser will extend within the reference plane. Preferably, the frame is further positionable, or the ball spotting laser is pivotally positionable within the frame, so that the ball spotting laser beam may extend to and illuminate the pool ball at the ball strike point.
The laser supporting frame preferably similarly supports a table spotting laser over the table surface so that the above described reference plane similarly bisects the table spotting laser, causing a table spotting laser beam emitted by the table spotting laser to similarly extend within the reference plane. The table spotting laser preferably points downwardly and forwardly at an acute angle from vertical, and directly toward a proper cut shot target point on the table surface. The cut shot target point necessarily lies within the reference plane, and is positioned rearwardly from the resting point of the pool ball a distance equal to the diameter of the pool ball.
Provided that the frame raises the table spotting and ball spotting lasers to elevations above the pool ball, the frame may acceptably hold the table spotting laser at varying locations within the above described reference plane. For example, the frame may acceptably hold the table spotting laser at elevations above or below the ball spotting laser, the frame may acceptably positively and forwardly offset the table spotting laser away from the ball spotting laser, or the frame may acceptably negatively and rearwardly offset the table spotting laser away from the ball spotting laser. Regardless of the frame""s placement of the table spotting laser within the reference plane, the following equation expresses the angular orientation of the table spotting laser in terms of the angular orientation of the ball spotting laser:       β    =                  tan                  -          1                    ⁡              (                                                            (                                  b                  -                  r                                )                            ⁢              tan              ⁢                              xe2x80x83                            ⁢              α                        -            r            -            o                    t                )              ,
where xcex2 equals the acute angle between a vertical line extending through the table spotting laser and a table spotting laser beam emitted by the table spotting laser, where b equals the elevation of the ball spotting laser over the table surface, where r equals the radius of the ball, where xcex1 equals the acute angle between a vertical line extending through the ball spotting laser and a ball spotting laser beam emitted by such laser, where o equals any positively forward or negatively rearward offset of the table spotting laser away from the vertical line extending through the ball spotting laser, and where t equals the elevation of the table spotting laser over the table surface. Conversely, the preferred angular orientation of the ball spotting laser may be expressed in terms of the angular orientation of the table spotting laser as follows:       α    =                  tan                  -          1                    ⁡              (                                            t              ⁢                              xe2x80x83                            ⁢              tan              ⁢                              xe2x80x83                            ⁢              β                        +            r            +            o                                b            -            r                          )              ,
all variables being defined as stated above. Preferably, the lateral offset o equals zero, the preferred frame holding the ball spotting and table spotting lasers in vertical alignment. Also preferably, the frame holds the ball spotting laser above the table spotting laser so that their laser beams do not cross. xcex1 and xcex2, as defined above, comprise a pair of angles which, when allowed to control the angular orientations of the ball spotting and table spotting lasers, assures illumination of the cut shot target point upon illumination of the ball strike point.
In operation of the assembly described above, and assuming that the frame rigidly holds the ball spotting and table spotting lasers in orientations as described above, the table spotting laser is turned on, and the frame is placed and positioned on the pool table""s table surface so that a ball spotting laser beam emitting therefrom is directed to the ball strike point upon a pool ball resting upon the table surface. The frame is then further positioned and aligned so that ball spotting laser beam extends forwardly within the reference plane described above. Thereafter, the table spotting laser is actuated, causing its table spotting laser beam to automatically illuminate the proper cut shot target point upon the table surface. The frame may be alternately configured so that it rests upon and extends upwardly from a floor surface. Alternately, the frame may be configured to rest upon the pool table""s raised side rail surface. The structures, geometries, and positioning steps discussed above are equally applicable to such alternate frame configurations.
Upon laser illumination of the cut shot target point, a novice pool player aims a pool cue stroke to drive a cue ball so that the cue ball rolls over the illuminated cut shot target point, resulting in proper striking of the pool ball at the ball strike point, driving the pool ball forwardly into the pocket.
Where the assembly of the instant invention consists exclusively of ball spotting and table spotting lasers supported by a frame, difficulties and inaccuracies may arise in aligning laser beams emitted by such lasers so that they extend within the above described reference plane, and further difficulties may arise in accurately pointing the ball spotting laser at the ball strike point. Such inaccuracies in aligning and pointing the lasers tend to cause the inventive assembly to illuminate a misplaced cut shot target point. In order to assist in achieving proper alignment of the ball spotting and table spotting lasers, a third laser having a fan beam collimation lens is preferably mounted upon the frame, such laser being oriented so that its beam fans vertically in alignment with light beams emitted by the ball spotting and table spotting lasers. In operation, such fanning and line drawing laser appears to draw an illuminated vertical line across structures such as the pool ball and the back wall of the pocket into which the pool ball is to be driven. Preferably, such line drawing laser is raised by the frame to an elevation allowing its fan beam to simultaneously draw vertical lines over the pool ball and over the back wall of the pocket. By aligning the frame so that such fan beam appears to draw a line which vertically bisects the pool ball, and which simultaneously intersects the pocket into which the pool ball is to be driven, proper alignment of the ball spotting and table spotting lasers is assured.
In order to assist in pointing the ball spotting laser at the ball strike point, a second line drawing laser, similarly having a fan beam collimation lens is preferably provided. Such second line drawing laser is preferably supported by a frame so that its beam fans horizontally at an elevation above the pool table""s table surface, such elevation being equal to the radius of the pool ball. Just as the properly aligned vertical line drawing laser appears to draw a line which vertically bisects the pool ball, the horizontal fan beam of such second line drawing laser appears to draw a line which horizontally bisects the pool ball. The intersection of such two bisecting lines accurately pre-illuminates the ball strike point. Upon pre-illumination of the ball strike point, the frame may be accurately manipulated to cause the ball spotting laser beam emitted by the ball spotting laser to further illuminate the ball strike point.
Preferably, the base of the frame is segmented, allowing a lower section of the base to support the horizontal line drawing laser, such segmentation allowing an upper section of the base of the frame to be alternately stacked upon the lower section, or placed upon the rail of the pool table. Where such segmented base configuration is adopted, the vertical dimension of the lower section of the base is necessarily equal to the elevation of the pool table""s side rail over the pool table""s surface.
The assemblies discussed and described above perform acceptably in pool cut shot training situations where the novice pool table is free to position the pool ball. However, where the inventive assembly is used to facilitate cut shot training during game play, situations may arise where the proper location of the frame, as described above, coincides with the location of another pool ball upon the table surface, or conflicts with other structures. In order to allow the inventive assembly to be effectively used during game play, the ball spotting and table spotting lasers are preferably pivotably mounted upon the frame, their axes of pivotal motion being perpendicular to the above described reference plane. Also preferably, a variable motion linkage interconnecting the ball spotting and table spotting lasers is provided, such linkage being adapted to assure that the angular orientations of the ball and table spotting lasers relate to each other in accordance with the equations set forth above.
A simple form of such variable motion linkage is manually executed by an operator or pool player, such operator directly pivoting the ball and table spotting lasers to radially align with prescribed visible indicia upon the frame or with tactilly detectable detents upon the frame, such indicia or detents being oriented so that they guide motions of the ball spotting and table spotting lasers in accordance with the equations set forth above.
Preferably, the variable motion linkage between the ball spotting and table spotting lasers provides continuous variability, facilitating alignment of the ball and table spotting lasers in a multiplicity of pairs of angles xcex1 and xcex2, each pair of angles relating to each other in accordance with the equations set forth above. The preferred continuously variable linkage advantageously lessens the constraints imposed by the geometry of the frame upon the required positioning of the frame.
A preferred continuously variable motion linkage comprises a cam and slide pin sub-assembly. Numerous other sub-assemblies for facilitating continuously variable angular motion of the ball and table spotting lasers may be utilized such as slide track and slide block assemblies, roller track and roller assemblies, slide slot and slide pin assemblies, paired non-circular gear assemblies, paired non-circular friction wheel assemblies, and computer controlled servo motor assemblies.
By pivotally mounting the ball and table spotting lasers upon the frame, and by providing a variable motion linkage which assures continuous proper angular orientation of the lasers, a ball spotting laser beam emanating from the ball spotting laser may be pointed at the ball strike point by pivotally moving the ball spotting laser with respect to the frame rather than forwardly and rearwardly moving the entire frame. The preferred segmented base configuration discussed above in relation to a fixed laser frame is equally applicable to the more preferred frame which supports the preferred pivotally mounted lasers.
Accordingly, it is an object of the present invention to provide structural assemblies and method steps as described above which assist in performance of pool cut shots through illumination upon a pool table""s surface of a cut shot target point.